Systems of Equations Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean to solve a system of equations graphically?

Back

Solving a system of equations graphically means finding the point(s) where the graphs of the equations intersect, which represents the solution(s) to the system.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by 'm'. It is calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the slope-intercept form of a linear equation (y = mx + b).

Front

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

y = -2/3x + 2.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the solution to a system of equations graphically?

Back

Plot both equations on the same graph and identify the point(s) where they intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system.

Front

What does it mean if two lines are coincident in a system of equations?

Back

If two lines are coincident, they lie on top of each other, meaning there are infinitely many solutions to the system.

Front

What is the significance of the point (1, 1) in a system of equations?

Back

The point (1, 1) is the solution to the system of equations if it is the point where the graphs of the equations intersect.